Illumination systems and microlithographic projection exposure apparatus are known. Systems of this type can operate with EUV illumination light having a wavelength of 13.6 nm. Currently light sources for systems of this type include plasma sources. Synchrotron radiation is an interesting alternative thereto. The known EUV lithography systems are usually equipped with Bragg mirrors as bundle-guiding components which are provided with coatings of individual layers having an optical thickness amounting to a fourth of the working wavelength, or coating systems derived therefrom. Coatings of this type often have a polarization-dependent effect. The polarization sensitivity of the optical components typically increases with increasing numerical aperture of the illumination or projection system as the finite angle at least of the marginal rays, which are incident at illumination angles that deviate the most from 90°, between the polarization vector and the illumination plane often can no longer be neglected. The creation of a high contrast ratio by illuminating a light-sensitive layer on a wafer or a substrate onto which a reticle structure, in other words a template, is projected using the projection exposure apparatus, can also depend on the polarization properties of the illumination light.